Laser MBE is a process especially useful for epitaxial layer-by-layer growth of ceramic thin films directly from sintered ceramic targets. By employing high vacuum MBE conditions, the process has a restriction in the controllability of chemical composition, e.g. nonstoi chiometry in oxides and nitrides, as compared with conventional pulsed laser deposition, but instead gains the possibility of in situ monitoring of surface reaction on an atomic scale by RHEED. Ever since our first success in observing RHEED intensity oscillation for CeO2 film growth on Si(l11), we have verified the molecular layer epitaxy by laser MBE for perovskite oxides (SrTiO3, BaTiO3, SrVO3 ,etc) and infinite-layer cuprates MCuO2 (M= Sr, Ba, Ca) on SrTiO3 substrates as well as for oxide and nitride films on Si substrates. Key factors to design the laser MBE system, operation parameters, and recent experimental results are presented and discussed.